In this paper we show how to use drift analysis in the case of two random variables $X_1, X_2$, when the drift is approximatively given by $A\cdot (X_1,X_2)^T$ for a matrix $A$. The non-trivial case is that $X_1$ and $X_2$ impede each other's progress, and we give a full characterization of this case. As application, we develop and analyze a minimal example TwoLinear of a dynamic environment that can be hard. The environment consists of two linear function $f_1$ and $f_2$ with positive weights $1$ and $n$, and in each generation selection is based on one of them at random. They only differ in the set of positions that have weight $1$ and $n$. We show that the $(1+1)$-EA with mutation rate $\chi/n$ is efficient for small $\chi$ on TwoLinear, but does not find the shared optimum in polynomial time for large $\chi$.

翻译：本文展示了如何对两个随机变量$X_1, X_2$进行漂移分析，其中漂移近似由矩阵$A$乘以$(X_1,X_2)^T$给出。非平凡情形是$X_1$和$X_2$相互阻碍对方的进展，我们对该情形给出了完整刻画。作为应用，我们构造并分析了一个动态环境的最小实例TwoLinear，该环境可能具有困难性。该环境包含两个线性函数$f_1$和$f_2$，其正权重分别为$1$和$n$，在每代选择中随机基于其中一个函数进行。这两个函数仅在权重为$1$和$n$的位置集合上存在差异。我们证明了：对于TwoLinear问题，采用突变率为$\chi/n$的(1+1)-EA在$\chi$较小时是高效的，但在$\chi$较大时无法在多项式时间内找到共享最优解。